@bertsmobile1 after stewing on things for a while, I watched some video of people replacing the gaskets on Kohler engines. Seemed simple enough, even more simple on a Kohler Courage (which is what I have). Then, I went out and took a closer look at the liquid on top of the muffler (took some pics too).
Looks like my valve cover is leaking... which makes sense, the oil in the valve cover sits and puddles in the bottom of the valve cover after I finish mowing. Then spends a day or two leaking onto the top of the muffler while the mower sits idle. Then, when I go to start it up, the muffler gets hot real fast and starts burning off the oil.
One thing that threw me off was that the internet was saying that burnt oil would be white... but, I think that is 'burnt clean oil', my mower is overdue for an oil change, so that is probably why my smoke is black.
Anyway, I also see a tiny leak at the head gasket too, although it is probably not bad enough that it needs to be fixed. I am going to go ahead and replace all of the gaskets so I can get some experience doing it, should be fun.
Main Leak onto muffler from valve cover
Discolored spot is a potential sign of a leak from head gasket, although it could just be spillage from the valve cover leak.